ALBANY — Senators said “I do” to gay marriage last night in a narrow 33-29 vote — making New York the sixth and largest state to allow same-sex couples to wed.

The groundbreaking vote set off a roar of approval from supporters in the Senate gallery — and a massive street party around the Stonewall Inn in Greenwich Village, the birthplace of the gay rights movement.

“I can’t believe this is happening — no words can say how I feel right now,” said an elated Eugene Lovendusky, 26, a Queens teacher who joined nearly 600 champagne-swilling, rainbow flag-waving celebrants in the streets around the bar.

At least one man wore a wedding gown — and more than few couples said they’d walk down the aisle as soon as possible.

“It’s great to no longer feel like a second-class citizen,” said an exuberant Tom Selty, 31, of Astoria, Queens,

At a party at the nearby Lesbian Gay Bisexual and Transgender Community Center, Martin Everall, 48, said the bill reflected that “We want what everyone else wants.”

Gov. Cuomo signed the bill into law at 11:55 p.m. last night. It will go into effect July 24.

The vote came after four members of the Senate’s GOP majority sided with 29 Democrats in a public roll call allowed by Senate Majority Leader Dean Skelos (R-Nassau) after two weeks of intense pressure by Cuomo and gay-rights groups.

“I’m very proud of New York and the statement it’s making to the nation today,” the governor told lawmakers in an unusual post-vote speech on the Senate floor.

But Diocese of Brooklyn Bishop Nicholas DiMarzio quickly blasted the bill last night, saying Cuomo and lawmakers had “deconstructed the single most important institution in human history.”

He said he asked all Catholic schools to refuse any “distinction or honors” from the governor or lawmakers who voted for the bill — and that schools “not invite any state legislator to speak or be present at any parish or school celebration.”

“They’re entitled to their religious beliefs, but they can’t use them to prevent someone else’s rights,” countered bill supporter Jeff Rutsky, 53, of Midwood, Brooklyn.